Horizontal fragmentation in distributed data bases

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database

distributed

Hello,
I study Horizontal Fragmentation in distributed data bases. I see phrase simple predicates.

Given R(A1, A2, .., An), a simple predicate pj is defined as "pj: Ai θ value", where θ є {=, <, ≤, >, ≥, ≠} and value є Di, where Di is the domain of Ai.
–
Examples:
PNAME = "Maintenance"
BUDGET ≤ 200000

A set of simple predicates may have two key properties

1. Completeness of Simple Predicates is

same minterm fragment have the same probability of being accessed by any application.

2. Minimality of Simple Predicates is

if p influences how fragmentation is performed (i.e., causes a fragment f to be further fragmented into fi and fj), then there should be at least one application that accesses fi and fj differently.

But, I need an example, on a simple fragmented table.
I can't understand them!
What is probability in Completeness or What is differently access in Minimality?
Thanks

What I have tried:

Understanding Completeness of Simple Predicates and Minimality of Simple Predicates in Horizontally fragmentation in Distributed data bases by an example.